A force F = 4 N acts on a body for Delta t = 4 s , and the…

A force $F = 4\ \mathrm{N}$ acts on a body for $\Delta t = 4\ \mathrm{s}$, and the body's speed changes by $\Delta v = 2\ \mathrm{m/s}$. What is its mass?

Explanation of Method

Mass from the impulse and the change of speed.

Step 1: Impulse–momentum theorem

\[ F\,\Delta t = m\,\Delta v \;\Longrightarrow\; m = \frac{F\,\Delta t}{\Delta v} = \frac{4 \cdot 4}{2}. \]

\[m = 8\ \mathrm{kg}\]

Check

$ a = F/m = 0.5\ \mathrm{m/s^2} $, $ \Delta v = a\,\Delta t = 0.5 \cdot 4 = 2\ \mathrm{m/s}\ \checkmark $

$F\ (\mathrm{N})$ $t\ (\mathrm{s})$ $0$ $2$ $4$ $6$ $4$ $J = F\,\Delta t = 16\ \mathrm{N\,s}$ $= m\,\Delta v \Rightarrow m = 8\ \mathrm{kg}$

Force against time. The shaded area is the impulse, 16 N·s; it equals the change of momentum $m\,\Delta v$.

Result

\[\boxed{\,m = 8\ \mathrm{kg}\,}\]